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    <title>Symmetric Venn diagrams</title>
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    <h1>Symmetric Venn diagrams</h1>

    <p>
        <img id="ellipses" src="ellipses.gif" 
            width="200" height="200" alt="Piecu elipshu diagramma">
    </p>

    <p>
    Here we show a Venn diagram made from 5 congruent ellipses. 
    The regions are colored according to the number of ellipses 
    in which they are contained. Note that the number of regions 
    colored with a given color corresponds to the appropriate 
    <em>binomial coefficient</em> (see table):  
    </p>

  <table class="matem">
    <tr> <td>#(white)</td>  <td>C<sub>5</sub><sup>0</sup> = 1</td> </tr>
    <tr> <td>#(yellow)</td>  <td>C<sub>5</sub><sup>1</sup> = 5</td> </tr>
    <tr> <td>#(red)</td>  <td>C<sub>5</sub><sup>2</sup> = 10</td> </tr>
    <tr> <td>#(blue)</td>  <td>C<sub>5</sub><sup>3</sup> = 10</td> </tr>
    <tr> <td>#(green)</td>  <td>C<sub>5</sub><sup>4</sup> = 5</td> </tr>
    <tr> <td>#(black)</td>  <td>C<sub>5</sub><sup>5</sup> = 1</td> </tr>
  </table>

    <p>
    This diagram has a <em>5-fold rotational symmetry</em>. 
    This means that there is a point <code>(x,y)</code> 
    about which the diagram may be 
    rotated by <code>2&pi;i/5</code> and remains invariant, for 
    <code>i=0,1,2,3,4</code>. 
    </p>

    <blockquote>
        <strong>Theorem.</strong>
        A necessary condition for the existence of an <code>n</code>-symmetric 
        diagram is that <code>n</code> be a prime number. 
    </blockquote>

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